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fuels, which are cheap and abundant.^10 Electric utilities in China and the United

States have begun development of underground coal gasification processes that

leave much of the pollutants and greenhouse gases such as carbon dioxide under

the ground. Over the next 20 years, China’s challenge is to provide enough elec-

tricity—the equivalent of the entire U.S. electrical grid—for some 300 million

people who will live in its newly developed cities and towns. Dependent on coal

and aware of the limitations of large-scale hydroelectric projects, China’s planners

are undertaking the world’s largest and most aggressive experiment in develop-

ing clean coal processes for generating electricity. Conservation, smarter elec-

tricity pricing, renewable energy sources, even nuclear power—these many

initiatives will all offer (limited) contributions to the world’s energy problems.

But how fast China travels down the clean-coal learning curve and how willingly

it shares its advances with the rest of the world are likely to prove definitive.

A SCHOOL BUSING PROBLEM Each year, a municipality contracts with a pri-

vate bus company for the transportation of students in the primary grades to and

from school. As a management consultant to the city, you must structure a bus-

ing plan. The city’s annual payment to the bus company will depend on the

number of “kid-miles” the company carries. (For instance, carrying 20 children

2 miles each amounts to 40 kid-miles, as does carrying 8 children 5 miles each.)

The city’s three elementary schools draw students from four distinct geo-

graphic neighborhoods. The city’s planning department has furnished figures

on the number of students in each neighborhood, the capacity of each school,

and the distance from each school to each neighborhood. Figure 17.7 shows a

map of the school district and provides the pertinent data. You must formulate

a busing plan that will minimize total transportation cost. Before turning to

the LP formulation and the computer solution in Table 17.2, try coming up

with an optimal bus plan on your own, using the information in Figure 17.7.

From the data in Figure 17.7, we can develop the following LP formulation:

Neighborhood

Enrollments

All decision variables are nonnegative.

S1S2S3 200

W1W2W3 400

E1E2E3 120

N1N2N3 240

N3E3W3S3 260

N2E2W2S2 400 School capacities

Subject to: N1E1W1S1 360

Minimize: 2.0N13.0E1.. .13.0W32.2S3

734 Chapter 17 Linear Programming

(^10) For a discussion of clean coal, see J. Fallows, “Dirty Coal, Clean Future,” The Atlantic(December
2010): 64–78.
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